Ferromagnetically coupled dimers on the distorted Shastry-Sutherland lattice: Application to (CuCl)LaNb2O7

A recent study [Tassel {\it et al.}, Phys. Rev. Lett. {\bf 105}, 167205 (2010)] has proposed a remarkable spin model for (CuCl)LaNb2O7, in which dimers are ferromagnetically coupled to each other on the distorted Shastry-Sutherland lattice. In this model, the intra-dimer exchange coupling J>0 is antiferromagnetic, while the inter-dimer exchange couplings are ferromagnetic and take different values, J_x,J_y<0, in the two bond directions. Anticipating that the highly frustrated character of this model may lead to a wide range of behaviors in (CuCl)LaNb2O7 and related compounds, we theoretically investigate the ground state phase diagram of this model in detail using the following three approaches: a strong-coupling expansion for small J_x and J_y, exact diagonalization for finite clusters, and a Schwinger boson mean field theory. When |J_x|, |J_y| <~ J, the system stays in a dimer singlet phase with a finite spin gap. This state is adiabatically connected to the decoupled-dimer limit J_x=J_y=0. We show that the magnetization process of this phase depends crucially on the spatial anisotropy of the inter-dimer couplings. The magnetization shows a jump or a smooth increase for weak and strong anisotropy, respectively, after the spin gap closes at a certain magnetic field. When |J_x| or |J_y| >~ J, quantum phase transitions to various magnetically ordered phases (ferromagnetic, collinear stripe, and spiral) occur. The Schwinger boson analysis demonstrates that quantum fluctuations split the classical degeneracy of different spiral ground states. Implications for (CuCl)LaNb2O7 and related compounds are discussed in light of our theoretical results and existing experimental data.Comment: 21 pages, 20 figure

Hahahahaha, Duuuuude, Yeeessss!: A two-parameter characterization of stretchable words and the dynamics of mistypings and misspellings

Stretched words like \u27heellllp\u27 or \u27heyyyyy\u27 are a regular feature of spoken language, often used to emphasize or exaggerate the underlying meaning of the root word. While stretched words are rarely found in formal written language and dictionaries, they are prevalent within social media. In this paper, we examine the frequency distributions of \u27stretchable words\u27 found in roughly 100 billion tweets authored over an 8 year period. We introduce two central parameters, \u27balance\u27 and \u27stretch\u27, that capture their main characteristics, and explore their dynamics by creating visual tools we call \u27balance plots\u27 and \u27spelling trees\u27. We discuss how the tools and methods we develop here could be used to study the statistical patterns of mistypings and misspellings and be used as a basis for other linguistic research involving stretchable words, along with the potential applications in augmenting dictionaries, improving language processing, and in any area where sequence construction matters, such as genetics

English verb regularization in books and tweets

The English language has evolved dramatically throughout its lifespan, to the extent that a modern speaker of Old English would be incomprehensible without translation. One concrete indicator of this process is the movement from irregular to regular (-ed) forms for the past tense of verbs. In this study we quantify the extent of verb regularization using two vastly disparate datasets: (1) Six years of published books scanned by Google (2003-2008), and (2) A decade of social media messages posted to Twitter (2008-2017). We find that the extent of verb regularization is greater on Twitter, taken as a whole, than in English Fiction books. Regularization is also greater for tweets geotagged in the United States relative to American English books, but the opposite is true for tweets geotagged in the United Kingdom relative to British English books. We also find interesting regional variations in regularization across counties in the United States. However, once differences in population are accounted for, we do not identify strong correlations with socio-demographic variables such as education or income

Crystallization and X-ray diffraction analysis of the C-terminal domain of the flax rust effector protein AvrM

The flax rust effector AvrM is a secreted protein of unknown fold that is recognized by the M resistance protein in flax. In order to investigate the structural basis of the AvrMM interaction and possible virulence-associated functions of AvrM, the C-terminal domains of two different AvrM variants (AvrM-A and avrM) were crystallized. Crystals of native AvrM-A were obtained using pentaerythritol ethoxylate (15/4 EO/OH) as a precipitant and diffracted X-rays to 2.9 angstrom resolution. Selenomethionine-derivative crystals of similar quality were obtained using PEG 1500 as a precipitant. Both the native and selenomethionine-labelled AvrM-A crystals had symmetry of space group C2221 with eight molecules in the asymmetric unit. Crystals of avrM had symmetry of space group P212121 and diffracted X-rays to 2.7 angstrom resolution. Initial AvrM-A phases were calculated using the single-wavelength anomalous dispersion (SAD) method and a partial model was built. Phases for avrM were obtained by molecular replacement using the partial AvrM-A model

Structures of Phytophthora RXLR Effector Proteins: a conserved but adaptable fold underpins functional diversity

Phytopathogens deliver effector proteins inside host plant cells to promote infection. These proteins can also be sensed by the plant immune system, leading to restriction of pathogen growth. Effector genes can display signatures of positive selection and rapid evolution, presumably a consequence of their co-evolutionary arms race with plants. The molecular mechanisms underlying how effectors evolve to gain new virulence functions and/or evade the plant immune system are poorly understood. Here, we report the crystal structures of the effector domains from two oomycete RXLR proteins, Phytophthora capsici AVR3a11 and Phytophthora infestans PexRD2. Despite sharin

Divergent Evolution of PcF/SCR74 Effectors in Oomycetes Is Associated with Distinct Recognition Patterns in Solanaceous Plants

Plants deploy cell surface receptors known as pattern-recognition re ceptors (PRRs) that recognize non-self molecules from pathogens and microbes to defend against invaders. PRRs typically recognize microbe-associated molecular patterns (MAMPs) that are usually widely conserved, some even across kingdoms. Here, we report an oomycete-specific family of small secreted cysteine-rich (SCR) proteins that displays divergent patterns of sequence variation in the Irish potato famine pathogen Phytophthora infestans. A subclass that includes the conserved effector PcF from Phytophthora cactorum activates immunity in a wide range of plant species. In contrast, the more diverse SCR74 subclass is specific to P. infestans and tends to trigger immune responses only in a limited number of wild potato genotypes. The SCR74 response was recently mapped to a G-type lectin receptor kinase (GLecRK) locus in the wild potato Solanum microdontum subsp. gigantophyllum. The G-LecRK locus displays a high diversity in Solanum host species compared to other solanaceous plants. We propose that the diversification of the SCR74 proteins in P. infestans is driven by a fast coevolutionary arms race with cell surface immune receptors in wild potato, which contrasts the presumed slower dynamics between conserved apoplastic effectors and PRRs. Understanding the molecular determinants of plant immune responses to these divergent molecular patterns in oomycetes is expected to contribute to deploying multiple layers of disease resistance in crop plants. IMPORTANCE Immune receptors at the plant cell surface can recognize invading microbes. The perceived microbial molecules are typically widely conserved and therefore the matching surface receptors can detect a broad spectrum of pathogens. Here we describe a family of Phytophthora small extracellular proteins that consists of conserved subfamilies that are widely recognized by solanaceous plants. Remarkably, one subclass of SCR74 proteins is highly diverse, restricted to the late blight pathogen Phytophthora infestans and is specifically detected in wild potato plants. The diversification of this subfamily exhibits signatures of a coevolutionary arms race with surface receptors in potato. Insights into the molecular interaction between these potato-specific receptors and the recognized Phytophthora proteins are expected to contribute to disease resistance breeding in potato